They will follow in the footsteps of Boreham Wood and Sutton United, who made history by competing north of the border last year.
Moors ended the season in second place after an eventful final day.
It is more reward for Tim Flowers and his side who had their best ever season.
Wrexham were beaten in the play-off Eliminator by Eastleigh but Bryan Hughes has accepted the invitation to compete.
Some 32 clubs will battle it out in the third round. Solihull and Wrexham will join teams from Northern Ireland and the Welsh League in competing.
They will sit alongside ten clubs from Ladbrokes Championship and 14 winners from the second round.
The draw for the first and second round will take place on Wednesday afternoon.